A general chemostat model with second-order Poisson jumps: asymptotic properties and application to industrial waste-water treatment
A chemostat is a laboratory device (of the bioreactor type) in which organisms (bacteria, phytoplankton) develop in a controlled manner. This paper studies the asymptotic properties of a chemostat model with generalized interference function and Poisson noise. Due to the complexity of abrupt and err...
| Main Authors: | , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2023-04-01
|
| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2023656?viewType=HTML |
| _version_ | 1797848247398563840 |
|---|---|
| author | Yassine Sabbar José Luis Diaz Palencia Mouhcine Tilioua Abraham Otero Anwar Zeb Salih Djilali |
| author_facet | Yassine Sabbar José Luis Diaz Palencia Mouhcine Tilioua Abraham Otero Anwar Zeb Salih Djilali |
| author_sort | Yassine Sabbar |
| collection | DOAJ |
| description | A chemostat is a laboratory device (of the bioreactor type) in which organisms (bacteria, phytoplankton) develop in a controlled manner. This paper studies the asymptotic properties of a chemostat model with generalized interference function and Poisson noise. Due to the complexity of abrupt and erratic fluctuations, we consider the effect of the second order Itô-Lévy processes. The dynamics of our perturbed system are determined by the value of the threshold parameter $ \mathfrak{C}^{\star}_0 $. If $ \mathfrak {C}^{\star}_0 $ is strictly positive, the stationarity and ergodicity properties of our model are verified (<i>practical scenario</i>). If $ \mathfrak {C}^{\star}_0 $ is strictly negative, the considered and modeled microorganism will disappear in an exponential manner. This research provides a comprehensive overview of the chemostat interaction under general assumptions that can be applied to various models in biology and ecology. In order to verify the reliability of our results, we probe the case of industrial waste-water treatment. It is concluded that higher order jumps possess a negative influence on the long-term behavior of microorganisms in the sense that they lead to complete extinction. |
| first_indexed | 2024-04-09T18:24:26Z |
| format | Article |
| id | doaj.art-7f6d3a8c4e5a4ecc9eb104ce55363d10 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-09T18:24:26Z |
| publishDate | 2023-04-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-7f6d3a8c4e5a4ecc9eb104ce55363d102023-04-12T01:13:37ZengAIMS PressAIMS Mathematics2473-69882023-04-0186130241304910.3934/math.2023656A general chemostat model with second-order Poisson jumps: asymptotic properties and application to industrial waste-water treatmentYassine Sabbar0José Luis Diaz Palencia1Mouhcine Tilioua2Abraham Otero 3Anwar Zeb4Salih Djilali51. MAIS Laboratory, MAMCS Group, FST Errachidia, Moulay Ismail University of Meknes, P. O. Box 509, Errachidia 52000, Morocco2. Department of Information Technology, Escuela Politecnica Superior, Universidad San Pablo-CEU, CEU Universities, Campus Monteprincipe, Boadilla del Monte, Madrid 28668, Spain 3. Department of Mathematics and Education, Universidad a Distancia de Madrid, Spain1. MAIS Laboratory, MAMCS Group, FST Errachidia, Moulay Ismail University of Meknes, P. O. Box 509, Errachidia 52000, Morocco2. Department of Information Technology, Escuela Politecnica Superior, Universidad San Pablo-CEU, CEU Universities, Campus Monteprincipe, Boadilla del Monte, Madrid 28668, Spain4. Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Abbottabad 22060, Khyber Pakhtunkhwa, Pakistan5. Faculty of Exact Sciences and Informatics, Mathematic Department, Hassiba Benbouali University, Chlef, AlgeriaA chemostat is a laboratory device (of the bioreactor type) in which organisms (bacteria, phytoplankton) develop in a controlled manner. This paper studies the asymptotic properties of a chemostat model with generalized interference function and Poisson noise. Due to the complexity of abrupt and erratic fluctuations, we consider the effect of the second order Itô-Lévy processes. The dynamics of our perturbed system are determined by the value of the threshold parameter $ \mathfrak{C}^{\star}_0 $. If $ \mathfrak {C}^{\star}_0 $ is strictly positive, the stationarity and ergodicity properties of our model are verified (<i>practical scenario</i>). If $ \mathfrak {C}^{\star}_0 $ is strictly negative, the considered and modeled microorganism will disappear in an exponential manner. This research provides a comprehensive overview of the chemostat interaction under general assumptions that can be applied to various models in biology and ecology. In order to verify the reliability of our results, we probe the case of industrial waste-water treatment. It is concluded that higher order jumps possess a negative influence on the long-term behavior of microorganisms in the sense that they lead to complete extinction. https://www.aimspress.com/article/doi/10.3934/math.2023656?viewType=HTMLchemostatpoisson jumpsdynamicsergodicitywaste-water treatment |
| spellingShingle | Yassine Sabbar José Luis Diaz Palencia Mouhcine Tilioua Abraham Otero Anwar Zeb Salih Djilali A general chemostat model with second-order Poisson jumps: asymptotic properties and application to industrial waste-water treatment AIMS Mathematics chemostat poisson jumps dynamics ergodicity waste-water treatment |
| title | A general chemostat model with second-order Poisson jumps: asymptotic properties and application to industrial waste-water treatment |
| title_full | A general chemostat model with second-order Poisson jumps: asymptotic properties and application to industrial waste-water treatment |
| title_fullStr | A general chemostat model with second-order Poisson jumps: asymptotic properties and application to industrial waste-water treatment |
| title_full_unstemmed | A general chemostat model with second-order Poisson jumps: asymptotic properties and application to industrial waste-water treatment |
| title_short | A general chemostat model with second-order Poisson jumps: asymptotic properties and application to industrial waste-water treatment |
| title_sort | general chemostat model with second order poisson jumps asymptotic properties and application to industrial waste water treatment |
| topic | chemostat poisson jumps dynamics ergodicity waste-water treatment |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023656?viewType=HTML |
| work_keys_str_mv | AT yassinesabbar ageneralchemostatmodelwithsecondorderpoissonjumpsasymptoticpropertiesandapplicationtoindustrialwastewatertreatment AT joseluisdiazpalencia ageneralchemostatmodelwithsecondorderpoissonjumpsasymptoticpropertiesandapplicationtoindustrialwastewatertreatment AT mouhcinetilioua ageneralchemostatmodelwithsecondorderpoissonjumpsasymptoticpropertiesandapplicationtoindustrialwastewatertreatment AT abrahamotero ageneralchemostatmodelwithsecondorderpoissonjumpsasymptoticpropertiesandapplicationtoindustrialwastewatertreatment AT anwarzeb ageneralchemostatmodelwithsecondorderpoissonjumpsasymptoticpropertiesandapplicationtoindustrialwastewatertreatment AT salihdjilali ageneralchemostatmodelwithsecondorderpoissonjumpsasymptoticpropertiesandapplicationtoindustrialwastewatertreatment AT yassinesabbar generalchemostatmodelwithsecondorderpoissonjumpsasymptoticpropertiesandapplicationtoindustrialwastewatertreatment AT joseluisdiazpalencia generalchemostatmodelwithsecondorderpoissonjumpsasymptoticpropertiesandapplicationtoindustrialwastewatertreatment AT mouhcinetilioua generalchemostatmodelwithsecondorderpoissonjumpsasymptoticpropertiesandapplicationtoindustrialwastewatertreatment AT abrahamotero generalchemostatmodelwithsecondorderpoissonjumpsasymptoticpropertiesandapplicationtoindustrialwastewatertreatment AT anwarzeb generalchemostatmodelwithsecondorderpoissonjumpsasymptoticpropertiesandapplicationtoindustrialwastewatertreatment AT salihdjilali generalchemostatmodelwithsecondorderpoissonjumpsasymptoticpropertiesandapplicationtoindustrialwastewatertreatment |